COOKEVILLE, Tennessee (CNN) --Police video released Wednesday showed a North Carolina family kneeling and handcuffed, who shrieked as officers killed their dog -- which appeared to be playfully wagging its tail -- with a shotgun during a traffic stop.

The Smoak family was pulled over the evening of January 1 on Interstate 40 in eastern Tennessee by officers who mistakenly suspected them of a carjacking. An investigation showed James Smoak had simply left his wallet on the roof of his car at a gas station, and motorists who saw his money fly off the car as he drove away called police.

The family was driving through eastern Tennessee on their way home from a New Year's trip to Nashville. They told CNN they are in the process of retaining a lawyer and considering legal action against the Cookeville, Tennessee, Police Department and the Tennessee Highway Patrol for what happened to them and their dog.

In the video, released by the THP, officers are heard ordering the family, one by one, to get out of their car with their hands up. James Smoak and his wife, Pamela, and 17-year-old son Brandon are ordered onto their knees and handcuffed.

"What did I do?" James Smoak asks the officers.

"Sir, inside information is that you was involved in some type of robbery in Davidson County," the unidentified officer says.

Smoak and his wife protest incredulously, telling the officers that they are from South Carolina and that their mother and father-in-law are traveling in another car alongside them.

The Smoaks told CNN that as they knelt, handcuffed, they pleaded with officers to close the doors of their car so their two dogs would not escape, but the officers did not heed them.

Pamela Smoak is seen on the tape looking up at an officer, telling him slowly, "That dog is not mean. He won't hurt you."

Her husband says, "I got a dog in the car. I don't want him to jump out."

The tape then shows the Smoak's medium-size brown dog romping on the shoulder of the Interstate, its tail wagging. As the family yells, the dog, named Patton, first heads away from the road, then quickly circles back toward the family.

An officer in a blue uniform aims his shotgun at the dog and fires at its head, killing it immediately.

For several moments, all that is audible are shrieks as the family reacts to the shooting. James Smoak even stands up, but officers pull him back down.

The officers bring him to the patrol car, and the family calms down, but still they ask the officers for an explanation. One of them says Patton was "going after" the officer.

"No he wasn't, man," James Smoak says. "Y'all didn't have to kill the dog like that."

Brandon told CNN Patton, was playful and gentle -- "like Scooby-Doo" -- and may have simply gone after the beam of the flashlight as he often did at home, when Brandon and the dog would play.

The Tennessee Department of Safety, which oversees the Highway Patrol, has said an investigation is under way.

Cookeville Police Chief Robert Terry released a statement on the department's Web site Wednesday night describing the department's regret over the incident.

"I know the officer wishes that circumstances could have been different so he could have prevented shooting the dog," Terry wrote. "It is never gratifying to have to put an animal down, especially a family pet, and the officer assures me that he never displayed any satisfaction in doing so."

Terry said he and the vice-mayor of Cookeville met with the family before they left "to convey our deepest sympathies" for the loss of their dog.

"No one wants to experience this kind of thing, and it's very unfortunate that it occurred," he wrote. "If we had the benefit of hindsight, I'm sure some -- if not all of this -- could have been avoided. I believe the Tennessee Highway Patrol feels the same way."

The department is conducting an investigation to determine what, if anything, could have been done differently, he said. Police also plan to be in contact with the Smoak family, Terry said.